This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
The perpendicular distance between the two chords is 19.21 cm. Here's how to calculate it: 1. Understand the geometry: A perpendicular from the center of a circle to a chord bisects the chord. We can form a right-angled triangle with the radius as the hypotenuse, half the chord length as one leg, and the perpendicular distance from the center to the chord as the other leg. 2. Calculate half-lengths of the chords: Half of chord 1 (c1/2) = 15.6 cm / 2 = 7.8 cm Half of chord 2 (c2/2) = 13 cm / 2 = 6.5 cm 3. Calculate the perpendicular distance from the center to each chord using the Pythagorean theorem (a² + b² = c²): For chord 1 (d1): Radius² = d1² + (c1/2)² 12² = d1² + 7.8² 144 = d1² + 60.84 d1² = 144 - 60.84 d1² = 83.16 d1 = √83.16 ≈ 9.1192 cm For chord 2 (d2): Radius² = d2² + (c2/2)² 12² = d2² + 6.5² 144 = d2² + 42.25 d2² = 144 - 42.25 d2² = 101.75 d2 = √101.75 ≈ 10.0871 cm 4. Calculate the total perpendicular distance between the two chords: Since the chords are on opposite sides of the center, the total distance is the sum of their individual distances from the center. Total distance = d1 + d2 Total distance = 9.1192 cm + 10.0871 cm Total distance = 19.2063 cm 5. Round to two decimal places: Total distance ≈ 19.21 cm